OFFSET
1,1
COMMENTS
Each term is created by calculating the sum of the digits of the previous number, and the product of its digits. The results are concatenated to give the new number. Starting with 8, the second number is 88. The third number is generated as follows: 8+8=16, 8x8=64, which gives 1664. Continuing this way, the 7th number in this sequence becomes 88, equal to the second number of the sequence. Therefore, the pattern 88, 1664, 17144, 17112, 1214, ... repeats itself indefinitely.
LINKS
Peter Kagey, Table of n, a(n) for n = 1..10000
MATHEMATICA
NestList[FromDigits@ Join[IntegerDigits@ Total@ #, IntegerDigits[Times @@ #]] &@ IntegerDigits@ # &, 8, 48] (* Michael De Vlieger, Aug 26 2016 *)
PadRight[{8}, 50, {1214, 88, 1664, 17144, 17112}] (* Harvey P. Dale, Oct 04 2017 *)
PROG
(Haskell)
a271268 = 8 : cycle [88, 1664, 17144, 17112, 1214]
-- Correction by Peter Kagey, Aug 25 2016
(Python)
from functools import reduce
from operator import mul
def product(seq):
return reduce(mul, seq, 1)
def conversion(n):
n = str(n)
return str(sum(int(i) for i in n)) + \
str(product(int(i) for i in n))
def a271268(n):
if n == 1:
return 8
else:
r = 8
while n > 1:
r = conversion(r)
n -= 1
return int(r)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Sander Claassen, Apr 03 2016
STATUS
approved